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This article is cited in 1 scientific paper (total in 1 paper)
On nonexistence of distance regular graphs with the intersection array $\{53,40,28,16;1,4,10,28\}$
A. A. Makhnev, M. P. Golubyatnikov Krasovskii Institute of Mathematics and Mechanics, 16 Sofia Kovalevskaya Street, 620108 Yekaterinburg, Russia
Abstract:
We consider $Q$-polynomial graphs of diameter $4.$ Apart from infinite series intersection arrays $\{m(2m+1),(m-1)(2m+1),m^2,$ $m;1,m,m-1,m(2m+1)\}$ there are the following admissible intersection arrays of $Q$-polynomial graphs of diameter $4$ with at most $4096$ vertices: $\{5,4,4,3;1,1,2,2\}$ (odd graph on $9$ vertices), $\{9,8,7,6;1,2,3,4\}$ (folded $9$-cube), $\{36,21,10,3;1,6,15,28\}$ (half $9$-cube), and $\{53,40,28,$ $16;1,4,10,28\}.$ In the paper it is proved that a distance regular graph with an intersection array $\{53,40,28,16;1,4,10,28\}$ does not exist. Bibliogr. 4.
Keywords:
$Q$-polynomial graph, distance regular graph.
Received: 31.03.2021 Revised: 06.05.2021 Accepted: 07.05.2021
Citation:
A. A. Makhnev, M. P. Golubyatnikov, “On nonexistence of distance regular graphs with the intersection array $\{53,40,28,16;1,4,10,28\}$”, Diskretn. Anal. Issled. Oper., 28:3 (2021), 38–48
Linking options:
https://www.mathnet.ru/eng/da1280 https://www.mathnet.ru/eng/da/v28/i3/p38
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Abstract page: | 158 | Full-text PDF : | 45 | References: | 19 | First page: | 8 |
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